1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2007 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_UNION_FIND_H |
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20 | #define LEMON_UNION_FIND_H |
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21 | |
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22 | //!\ingroup auxdat |
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23 | //!\file |
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24 | //!\brief Union-Find data structures. |
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25 | //! |
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26 | |
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27 | #include <vector> |
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28 | #include <list> |
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29 | #include <utility> |
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30 | #include <algorithm> |
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31 | |
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32 | #include <lemon/bits/invalid.h> |
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33 | |
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34 | namespace lemon { |
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35 | |
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36 | /// \ingroup auxdat |
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37 | /// |
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38 | /// \brief A \e Union-Find data structure implementation |
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39 | /// |
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40 | /// The class implements the \e Union-Find data structure. |
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41 | /// The union operation uses rank heuristic, while |
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42 | /// the find operation uses path compression. |
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43 | /// This is a very simple but efficient implementation, providing |
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44 | /// only four methods: join (union), find, insert and size. |
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45 | /// For more features see the \ref UnionFindEnum class. |
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46 | /// |
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47 | /// It is primarily used in Kruskal algorithm for finding minimal |
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48 | /// cost spanning tree in a graph. |
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49 | /// \sa kruskal() |
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50 | /// |
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51 | /// \pre You need to add all the elements by the \ref insert() |
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52 | /// method. |
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53 | template <typename _ItemIntMap> |
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54 | class UnionFind { |
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55 | public: |
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56 | |
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57 | typedef _ItemIntMap ItemIntMap; |
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58 | typedef typename ItemIntMap::Key Item; |
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59 | |
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60 | private: |
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61 | // If the items vector stores negative value for an item then |
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62 | // that item is root item and it has -items[it] component size. |
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63 | // Else the items[it] contains the index of the parent. |
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64 | std::vector<int> items; |
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65 | ItemIntMap& index; |
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66 | |
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67 | bool rep(int idx) const { |
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68 | return items[idx] < 0; |
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69 | } |
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70 | |
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71 | int repIndex(int idx) const { |
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72 | int k = idx; |
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73 | while (!rep(k)) { |
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74 | k = items[k] ; |
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75 | } |
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76 | while (idx != k) { |
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77 | int next = items[idx]; |
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78 | const_cast<int&>(items[idx]) = k; |
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79 | idx = next; |
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80 | } |
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81 | return k; |
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82 | } |
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83 | |
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84 | public: |
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85 | |
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86 | /// \brief Constructor |
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87 | /// |
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88 | /// Constructor of the UnionFind class. You should give an item to |
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89 | /// integer map which will be used from the data structure. If you |
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90 | /// modify directly this map that may cause segmentation fault, |
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91 | /// invalid data structure, or infinite loop when you use again |
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92 | /// the union-find. |
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93 | UnionFind(ItemIntMap& m) : index(m) {} |
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94 | |
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95 | /// \brief Returns the index of the element's component. |
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96 | /// |
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97 | /// The method returns the index of the element's component. |
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98 | /// This is an integer between zero and the number of inserted elements. |
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99 | /// |
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100 | int find(const Item& a) { |
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101 | return repIndex(index[a]); |
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102 | } |
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103 | |
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104 | /// \brief Clears the union-find data structure |
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105 | /// |
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106 | /// Erase each item from the data structure. |
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107 | void clear() { |
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108 | items.clear(); |
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109 | } |
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110 | |
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111 | /// \brief Inserts a new element into the structure. |
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112 | /// |
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113 | /// This method inserts a new element into the data structure. |
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114 | /// |
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115 | /// The method returns the index of the new component. |
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116 | int insert(const Item& a) { |
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117 | int n = items.size(); |
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118 | items.push_back(-1); |
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119 | index.set(a,n); |
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120 | return n; |
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121 | } |
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122 | |
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123 | /// \brief Joining the components of element \e a and element \e b. |
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124 | /// |
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125 | /// This is the \e union operation of the Union-Find structure. |
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126 | /// Joins the component of element \e a and component of |
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127 | /// element \e b. If \e a and \e b are in the same component then |
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128 | /// it returns false otherwise it returns true. |
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129 | bool join(const Item& a, const Item& b) { |
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130 | int ka = repIndex(index[a]); |
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131 | int kb = repIndex(index[b]); |
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132 | |
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133 | if ( ka == kb ) |
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134 | return false; |
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135 | |
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136 | if (items[ka] < items[kb]) { |
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137 | items[ka] += items[kb]; |
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138 | items[kb] = ka; |
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139 | } else { |
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140 | items[kb] += items[ka]; |
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141 | items[ka] = kb; |
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142 | } |
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143 | return true; |
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144 | } |
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145 | |
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146 | /// \brief Returns the size of the component of element \e a. |
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147 | /// |
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148 | /// Returns the size of the component of element \e a. |
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149 | int size(const Item& a) { |
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150 | int k = repIndex(index[a]); |
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151 | return - items[k]; |
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152 | } |
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153 | |
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154 | }; |
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155 | |
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156 | /// \ingroup auxdat |
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157 | /// |
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158 | /// \brief A \e Union-Find data structure implementation which |
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159 | /// is able to enumerate the components. |
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160 | /// |
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161 | /// The class implements a \e Union-Find data structure |
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162 | /// which is able to enumerate the components and the items in |
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163 | /// a component. If you don't need this feature then perhaps it's |
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164 | /// better to use the \ref UnionFind class which is more efficient. |
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165 | /// |
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166 | /// The union operation uses rank heuristic, while |
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167 | /// the find operation uses path compression. |
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168 | /// |
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169 | /// \pre You need to add all the elements by the \ref insert() |
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170 | /// method. |
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171 | /// |
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172 | template <typename _ItemIntMap> |
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173 | class UnionFindEnum { |
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174 | public: |
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175 | |
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176 | typedef _ItemIntMap ItemIntMap; |
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177 | typedef typename ItemIntMap::Key Item; |
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178 | |
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179 | private: |
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180 | |
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181 | // If the parent stores negative value for an item then that item |
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182 | // is root item and it has -items[it].parent component size. Else |
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183 | // the items[it].parent contains the index of the parent. |
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184 | // |
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185 | // The \c nextItem and \c prevItem provides the double-linked |
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186 | // cyclic list of one component's items. The \c prevClass and |
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187 | // \c nextClass gives the double linked list of the representant |
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188 | // items. |
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189 | struct ItemT { |
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190 | int parent; |
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191 | Item item; |
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192 | |
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193 | int nextItem, prevItem; |
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194 | int nextClass, prevClass; |
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195 | }; |
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196 | |
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197 | std::vector<ItemT> items; |
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198 | ItemIntMap& index; |
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199 | |
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200 | int firstClass; |
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201 | |
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202 | |
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203 | bool rep(int idx) const { |
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204 | return items[idx].parent < 0; |
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205 | } |
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206 | |
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207 | int repIndex(int idx) const { |
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208 | int k = idx; |
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209 | while (!rep(k)) { |
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210 | k = items[k].parent; |
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211 | } |
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212 | while (idx != k) { |
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213 | int next = items[idx].parent; |
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214 | const_cast<int&>(items[idx].parent) = k; |
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215 | idx = next; |
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216 | } |
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217 | return k; |
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218 | } |
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219 | |
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220 | void unlaceClass(int k) { |
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221 | if (items[k].prevClass != -1) { |
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222 | items[items[k].prevClass].nextClass = items[k].nextClass; |
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223 | } else { |
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224 | firstClass = items[k].nextClass; |
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225 | } |
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226 | if (items[k].nextClass != -1) { |
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227 | items[items[k].nextClass].prevClass = items[k].prevClass; |
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228 | } |
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229 | } |
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230 | |
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231 | void spliceItems(int ak, int bk) { |
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232 | items[items[ak].prevItem].nextItem = bk; |
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233 | items[items[bk].prevItem].nextItem = ak; |
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234 | int tmp = items[ak].prevItem; |
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235 | items[ak].prevItem = items[bk].prevItem; |
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236 | items[bk].prevItem = tmp; |
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237 | |
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238 | } |
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239 | |
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240 | public: |
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241 | |
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242 | UnionFindEnum(ItemIntMap& _index) |
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243 | : items(), index(_index), firstClass(-1) {} |
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244 | |
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245 | /// \brief Inserts the given element into a new component. |
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246 | /// |
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247 | /// This method creates a new component consisting only of the |
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248 | /// given element. |
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249 | /// |
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250 | void insert(const Item& item) { |
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251 | ItemT t; |
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252 | |
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253 | int idx = items.size(); |
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254 | index.set(item, idx); |
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255 | |
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256 | t.nextItem = idx; |
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257 | t.prevItem = idx; |
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258 | t.item = item; |
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259 | t.parent = -1; |
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260 | |
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261 | t.nextClass = firstClass; |
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262 | if (firstClass != -1) { |
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263 | items[firstClass].prevClass = idx; |
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264 | } |
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265 | t.prevClass = -1; |
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266 | firstClass = idx; |
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267 | |
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268 | items.push_back(t); |
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269 | } |
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270 | |
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271 | /// \brief Inserts the given element into the component of the others. |
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272 | /// |
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273 | /// This methods inserts the element \e a into the component of the |
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274 | /// element \e comp. |
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275 | void insert(const Item& item, const Item& comp) { |
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276 | int k = repIndex(index[comp]); |
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277 | ItemT t; |
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278 | |
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279 | int idx = items.size(); |
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280 | index.set(item, idx); |
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281 | |
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282 | t.prevItem = k; |
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283 | t.nextItem = items[k].nextItem; |
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284 | items[items[k].nextItem].prevItem = idx; |
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285 | items[k].nextItem = idx; |
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286 | |
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287 | t.item = item; |
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288 | t.parent = k; |
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289 | |
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290 | --items[k].parent; |
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291 | |
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292 | items.push_back(t); |
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293 | } |
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294 | |
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295 | /// \brief Clears the union-find data structure |
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296 | /// |
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297 | /// Erase each item from the data structure. |
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298 | void clear() { |
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299 | items.clear(); |
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300 | firstClass = -1; |
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301 | } |
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302 | |
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303 | /// \brief Finds the leader of the component of the given element. |
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304 | /// |
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305 | /// The method returns the leader of the component of the given element. |
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306 | const Item& find(const Item &item) const { |
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307 | return items[repIndex(index[item])].item; |
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308 | } |
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309 | |
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310 | /// \brief Joining the component of element \e a and element \e b. |
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311 | /// |
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312 | /// This is the \e union operation of the Union-Find structure. |
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313 | /// Joins the component of element \e a and component of |
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314 | /// element \e b. If \e a and \e b are in the same component then |
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315 | /// returns false else returns true. |
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316 | bool join(const Item& a, const Item& b) { |
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317 | |
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318 | int ak = repIndex(index[a]); |
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319 | int bk = repIndex(index[b]); |
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320 | |
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321 | if (ak == bk) { |
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322 | return false; |
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323 | } |
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324 | |
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325 | if ( items[ak].parent < items[bk].parent ) { |
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326 | unlaceClass(bk); |
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327 | items[ak].parent += items[bk].parent; |
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328 | items[bk].parent = ak; |
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329 | } else { |
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330 | unlaceClass(ak); |
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331 | items[bk].parent += items[ak].parent; |
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332 | items[ak].parent = bk; |
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333 | } |
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334 | spliceItems(ak, bk); |
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335 | |
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336 | return true; |
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337 | } |
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338 | |
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339 | /// \brief Returns the size of the component of element \e a. |
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340 | /// |
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341 | /// Returns the size of the component of element \e a. |
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342 | int size(const Item &item) const { |
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343 | return - items[repIndex(index[item])].parent; |
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344 | } |
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345 | |
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346 | /// \brief Splits up the component of the element. |
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347 | /// |
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348 | /// Splitting the component of the element into sigleton |
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349 | /// components (component of size one). |
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350 | void split(const Item &item) { |
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351 | int k = repIndex(index[item]); |
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352 | int idx = items[k].nextItem; |
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353 | while (idx != k) { |
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354 | int next = items[idx].nextItem; |
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355 | |
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356 | items[idx].parent = -1; |
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357 | items[idx].prevItem = idx; |
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358 | items[idx].nextItem = idx; |
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359 | |
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360 | items[idx].nextClass = firstClass; |
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361 | items[firstClass].prevClass = idx; |
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362 | firstClass = idx; |
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363 | |
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364 | idx = next; |
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365 | } |
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366 | |
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367 | items[idx].parent = -1; |
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368 | items[idx].prevItem = idx; |
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369 | items[idx].nextItem = idx; |
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370 | |
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371 | items[firstClass].prevClass = -1; |
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372 | } |
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373 | |
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374 | /// \brief Sets the given element to the leader element of its component. |
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375 | /// |
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376 | /// Sets the given element to the leader element of its component. |
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377 | void makeRep(const Item &item) { |
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378 | int nk = index[item]; |
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379 | int k = repIndex(nk); |
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380 | if (nk == k) return; |
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381 | |
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382 | if (items[k].prevClass != -1) { |
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383 | items[items[k].prevClass].nextClass = nk; |
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384 | } else { |
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385 | firstClass = nk; |
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386 | } |
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387 | if (items[k].nextClass != -1) { |
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388 | items[items[k].nextClass].prevClass = nk; |
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389 | } |
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390 | |
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391 | int idx = items[k].nextItem; |
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392 | while (idx != k) { |
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393 | items[idx].parent = nk; |
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394 | idx = items[idx].nextItem; |
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395 | } |
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396 | |
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397 | items[nk].parent = items[k].parent; |
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398 | items[k].parent = nk; |
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399 | } |
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400 | |
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401 | /// \brief Removes the given element from the structure. |
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402 | /// |
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403 | /// Removes the element from its component and if the component becomes |
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404 | /// empty then removes that component from the component list. |
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405 | /// |
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406 | /// \warning It is an error to remove an element which is not in |
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407 | /// the structure. |
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408 | void erase(const Item &item) { |
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409 | int idx = index[item]; |
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410 | if (rep(idx)) { |
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411 | int k = idx; |
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412 | if (items[k].parent == -1) { |
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413 | unlaceClass(idx); |
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414 | return; |
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415 | } else { |
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416 | int nk = items[k].nextItem; |
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417 | if (items[k].prevClass != -1) { |
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418 | items[items[k].prevClass].nextClass = nk; |
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419 | } else { |
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420 | firstClass = nk; |
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421 | } |
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422 | if (items[k].nextClass != -1) { |
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423 | items[items[k].nextClass].prevClass = nk; |
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424 | } |
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425 | |
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426 | int l = items[k].nextItem; |
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427 | while (l != k) { |
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428 | items[l].parent = nk; |
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429 | l = items[l].nextItem; |
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430 | } |
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431 | |
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432 | items[nk].parent = items[k].parent + 1; |
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433 | } |
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434 | } else { |
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435 | |
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436 | int k = repIndex(idx); |
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437 | idx = items[k].nextItem; |
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438 | while (idx != k) { |
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439 | items[idx].parent = k; |
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440 | idx = items[idx].nextItem; |
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441 | } |
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442 | |
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443 | ++items[k].parent; |
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444 | } |
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445 | |
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446 | idx = index[item]; |
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447 | items[items[idx].prevItem].nextItem = items[idx].nextItem; |
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448 | items[items[idx].nextItem].prevItem = items[idx].prevItem; |
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449 | |
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450 | } |
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451 | |
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452 | /// \brief Moves the given element to another component. |
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453 | /// |
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454 | /// This method moves the element \e a from its component |
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455 | /// to the component of \e comp. |
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456 | /// If \e a and \e comp are in the same component then |
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457 | /// it returns false otherwise it returns true. |
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458 | bool move(const Item &item, const Item &comp) { |
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459 | if (repIndex(index[item]) == repIndex(index[comp])) return false; |
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460 | erase(item); |
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461 | insert(item, comp); |
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462 | return true; |
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463 | } |
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464 | |
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465 | |
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466 | /// \brief Removes the component of the given element from the structure. |
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467 | /// |
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468 | /// Removes the component of the given element from the structure. |
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469 | /// |
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470 | /// \warning It is an error to give an element which is not in the |
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471 | /// structure. |
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472 | void eraseClass(const Item &item) { |
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473 | unlaceClass(repIndex(index[item])); |
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474 | } |
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475 | |
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476 | /// \brief Lemon style iterator for the representant items. |
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477 | /// |
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478 | /// ClassIt is a lemon style iterator for the components. It iterates |
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479 | /// on the representant items of the classes. |
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480 | class ClassIt { |
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481 | public: |
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482 | /// \brief Constructor of the iterator |
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483 | /// |
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484 | /// Constructor of the iterator |
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485 | ClassIt(const UnionFindEnum& ufe) : unionFind(&ufe) { |
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486 | idx = unionFind->firstClass; |
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487 | } |
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488 | |
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489 | /// \brief Constructor to get invalid iterator |
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490 | /// |
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491 | /// Constructor to get invalid iterator |
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492 | ClassIt(Invalid) : unionFind(0), idx(-1) {} |
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493 | |
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494 | /// \brief Increment operator |
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495 | /// |
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496 | /// It steps to the next representant item. |
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497 | ClassIt& operator++() { |
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498 | idx = unionFind->items[idx].nextClass; |
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499 | return *this; |
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500 | } |
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501 | |
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502 | /// \brief Conversion operator |
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503 | /// |
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504 | /// It converts the iterator to the current representant item. |
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505 | operator const Item&() const { |
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506 | return unionFind->items[idx].item; |
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507 | } |
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508 | |
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509 | /// \brief Equality operator |
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510 | /// |
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511 | /// Equality operator |
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512 | bool operator==(const ClassIt& i) { |
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513 | return i.idx == idx; |
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514 | } |
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515 | |
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516 | /// \brief Inequality operator |
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517 | /// |
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518 | /// Inequality operator |
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519 | bool operator!=(const ClassIt& i) { |
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520 | return i.idx != idx; |
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521 | } |
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522 | |
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523 | private: |
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524 | const UnionFindEnum* unionFind; |
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525 | int idx; |
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526 | }; |
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527 | |
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528 | /// \brief Lemon style iterator for the items of a component. |
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529 | /// |
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530 | /// ClassIt is a lemon style iterator for the components. It iterates |
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531 | /// on the items of a class. By example if you want to iterate on |
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532 | /// each items of each classes then you may write the next code. |
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533 | ///\code |
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534 | /// for (ClassIt cit(ufe); cit != INVALID; ++cit) { |
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535 | /// std::cout << "Class: "; |
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536 | /// for (ItemIt iit(ufe, cit); iit != INVALID; ++iit) { |
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537 | /// std::cout << toString(iit) << ' ' << std::endl; |
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538 | /// } |
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539 | /// std::cout << std::endl; |
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540 | /// } |
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541 | ///\endcode |
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542 | class ItemIt { |
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543 | public: |
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544 | /// \brief Constructor of the iterator |
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545 | /// |
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546 | /// Constructor of the iterator. The iterator iterates |
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547 | /// on the class of the \c item. |
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548 | ItemIt(const UnionFindEnum& ufe, const Item& item) : unionFind(&ufe) { |
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549 | idx = unionFind->repIndex(unionFind->index[item]); |
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550 | } |
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551 | |
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552 | /// \brief Constructor to get invalid iterator |
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553 | /// |
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554 | /// Constructor to get invalid iterator |
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555 | ItemIt(Invalid) : unionFind(0), idx(-1) {} |
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556 | |
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557 | /// \brief Increment operator |
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558 | /// |
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559 | /// It steps to the next item in the class. |
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560 | ItemIt& operator++() { |
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561 | idx = unionFind->items[idx].nextItem; |
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562 | if (unionFind->rep(idx)) idx = -1; |
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563 | return *this; |
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564 | } |
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565 | |
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566 | /// \brief Conversion operator |
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567 | /// |
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568 | /// It converts the iterator to the current item. |
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569 | operator const Item&() const { |
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570 | return unionFind->items[idx].item; |
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571 | } |
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572 | |
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573 | /// \brief Equality operator |
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574 | /// |
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575 | /// Equality operator |
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576 | bool operator==(const ItemIt& i) { |
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577 | return i.idx == idx; |
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578 | } |
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579 | |
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580 | /// \brief Inequality operator |
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581 | /// |
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582 | /// Inequality operator |
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583 | bool operator!=(const ItemIt& i) { |
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584 | return i.idx != idx; |
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585 | } |
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586 | |
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587 | private: |
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588 | const UnionFindEnum* unionFind; |
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589 | int idx; |
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590 | }; |
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591 | |
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592 | }; |
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593 | |
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594 | |
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595 | //! @} |
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596 | |
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597 | } //namespace lemon |
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598 | |
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599 | #endif //LEMON_UNION_FIND_H |
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